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Physical Review A

Shannon entropy and the eigenstates of the single-mode squeeze operator

C. G. Bollini, L. E. Oxman

Published Mar 1, 1993• 25 citations
Publisher

Abstract

The interaction Hamiltonian for the degenerate parametric amplifier leads to an eigenvalue equation which can be solved. The solution is used to construct the propagation kernel for the state vectors. We can then follow the evolution of the squeezed variable and its conjugate one. Also the changes of entropies during the process can be followed without difficulties.

DOI
10.1103/physreva.47.2339

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•Feb 1, 1992•0 citations
The interaction Hamiltonian for the degenerate parametric amplifier leads to an eigenvalue equation which can be solved. The solution is used to construct the propagation kernel for the state vectors. We can then follow the evolution of the squeezed variable and its conjugate one. Also the changes of entropies during the process can be followed without difficulties.
Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.